I've been looking around a few places to try to understand some notation. I'm not sure exactly what to call it(set notation?) but basically things like g: [a, b] → R and stuff like that. I think it means something like g is defined on [a,b] in the real numbers, but is there a resource I can use...
Your junior schedule is almost identical to my junior schedule from last year, although my school doesn't offer Physics C. AP Chem isn't actually that bad. I had a terrible teacher and I still managed to 5 the exam with the only prep outside of the classroom being the weekend before the exam. I...
Thanks. Is there a practical downside to not being able to take non-major courses, or is it simply a case of not being able to pursue some minor interests?
I think "for" isn't the best word, something like "in" or "over" would be better. A Newton meter(joule) is equivalent to the change in energy that results from applying a force of one Newton over a distance of one meter. A Newton/meter would be applicable if you were pushing an object by adding...
I think it depends on what you mean when you say vectors. To me, you could mean anything from fairly basic concepts, like addition, direction and resolution as discussed in introductory physics, to some more advanced vector algebra, like products and projections, to vector calculus. If you mean...
I'm currently beginning my senior year in high school and I have been struggling for the last year or so to figure out what I want to do in college. I find a lot of things interesting, and so it's hard for me to pinpoint a single area of study in STEM that I would want to pursue. After a lot of...
Well the reason why 2 meters PER second works so well is that you are measuring the number of meters it takes you to go in a second and the way you do that mathematically is by dividing the number of meters by the number of seconds. And who says multiplication doesn't yield anything meaningful...
Is the statement that energy is proportional to Fdx an assumption? I just showed that the left hand quantity is proportional to Fdx, and that is what I defined to be the kinetic energy.
A simple derivation of W \propto v^2? I always thought energy was just a convenient quantity that we defined from the following:
From kinematics we have v_f^2- v_i^2 =2a \Delta x
Multiplying through by \frac{1}{2}m gives \frac{1}{2}m(v_f^2-v_i^2) = \Delta (\frac{1}{2}mv^2) = ma \Delta x = F...
My physics teacher cooked up an experiment today on the fly where we tried to calculate the horizontal distance traveled, D, from a rubber tube through which water was siphoned from a graduated cylinder elevated a certain distance H from the ground:
He modified an experiment he had found of...
The issue I found with that is that h drops out of the equation once y=0 with x substituted is differentiated implicitly with respect to theta. I managed to solve the equation with Lagrange multipliers with the following:
\nabla x = \lambda \nabla y so \frac{\partial x}{\partial \theta} =...
I don't think I can substitute t into the y equation since I'm trying to maximize x and I need to solve for t when y=0.
Here is my work so far:
y(t)= h+v_0sin(\theta)t -\frac{1}{2}gt^2=0
t= \frac{-v_0sin(\theta)\pm \sqrt{v_0^2sin^2(\theta) +2gh}}{-g} and disregarding the negative solution...